ReachBal or double harmonic/Gypsy major — a Reach heptatonality
Tonalibus 2b-5 reach – 2023-01 – 15x
Tonalibus 2b-5 reach – 2021-04 – 20
Tonalibus 2b-5 reach – 2021-04 – 21
Scale and sound samples
- Reach or harmonic tonality matrix: The octave includes one or exceptionally two (double harmonic) Reach steps (augmented seconds) framed by half steps (or semitones) or exceptionally by a whole and a half step. There are either three whole steps or exceptionally just one. If three of them, they are in most cases either a pair and a single one separated by the third half step, or a trio framed by half steps. Exceptionally though all three whole steps are singles. When a trio of consecutive whole steps, they are preceded or followed by two consecutive half steps. The total number of half steps is three, or exceptionally four with two (double harmonic) Reach steps.
- ReachBal: The name underlines balance in pitch distribution and indicates that there are two Reach steps, one in the lower, the other in the upper tetrachord. A.k.a. harmonic minor over Phrygian major.
- Step pattern: Ascending from the fundamental (tonic or Do), a half step leads to a Reach step, followed by another half step. Then comes a whole step, a half step, a second Reach step, plus finally a fourth half step leading up to the octave. The octave is in the midst of two successive half steps.
- Scale intervals: Minor second, major third, quart, quint, minor sixth, and major seventh.
- Tetra- or pentachords: The lower as well as the upper are both harmonic or Reach.
- Harmonic axes: There are two axes at symmetrical angles, NE-SW and NW-SE.
- Primary harmonic anchors: The fundamental or North anchor is fully present. The contrast or South anchor is represented by both its legs but no head. East and West anchors each contribute one leg, the East its left and the West its right one.
- Secondary harmonic anchors: There are no secondary anchors present.
- Overall balance and symmetry: Placement of pitches, intervals, and axes of East and West mirror each other. This results in a striking balance between very pronounced regressive and progressive, as well as major and minor elements.